We also visualized the confidence sequences of the algorithms studied in this paper and PRECiSE in Figures REF  and REF .We do not compare with the methods of [1]}, since our main focus is on developing an efficient, yet tight approximation of UP; instead, we refer an interested reader to the experiments of [2]}.
Similar to the experiment settings in [2]}, and [1]} in turn, we considered i.i.d. processes under Bern(0.5), Beta(1,1), Beta(10,10) (in Figure REF ), Bern(0.25), Beta(1,3), and Beta(10,30) (in Figure REF ) distributions.
Here, CB is a naive method based on an alternative odds vector construction \({\bf x}_t\leftarrow [1-Y_t+m, 1+Y_t-m]\) , which can be viewed as running the continuous coin betting; cf. (REF ) and see Table REF .
We include this simple baseline to highlight the effect of the form of gambling in constructing confidence sequences.
We used the uniform prior for the UP and the UP component in the hybrid algorithms, and used \(t_{\texttt {UP}}=50\)  for the hybrid algorithm (REF ).
